It really depends. Is it a matter of surviving for a week (plenty of food and cloths seem to say it isn't, unless there are predators on the island), or a test to live for a week outside the tech bubble. In the first case, we need survival tools, so something like a Swiss knife, a weapon (but I wouldn't know how to use it) or an axe, a recipient to keep drinking liquid in. If it's just a test to live outside the tech bubble for a week, and the island has the necessary comfort except tech, I would bring pen, paper, and a... ball, I think.